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(B) Since particle $C$ is moved without any acceleration,the change in kinetic energy is zero,$\Delta K.E. = 0$.By the work-energy theorem,the work do

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$\frac{2 G M m}{r}$

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(B) Since particle $C$ is moved without any acceleration,the change in kinetic energy is zero,$\Delta K.E. = 0$.By the work-energy theorem,the work done by an external agent plus the work done by gravitational forces is zero: $W_{	ext{ext}} + W_{	ext{grav}} = 0$.Therefore,$W_{	ext{ext}} = -W_{	ext{grav}} = \Delta U = U_f - U_i$.The gravitational potential energy of the system involving particle $C$ is $U = -\frac{GMm}{r_A} - \frac{GMm}{r_B}$,where $r_A$ and $r_B$ are the distances of $C$ from $A$ and $B$ respectively.Initial position: $C$ is at the midpoint,so $r_A = r/2$ and $r_B = r/2$.$U_i = -\frac{GMm}{r/2} - \frac{GMm}{r/2} = -\frac{2GMm}{r} - \frac{2GMm}{r} = -\frac{4GMm}{r}$.Final position: $C$ is at a point equidistant $r$ from $A$ and $B$,so $r_A = r$ and $r_B = r$.$U_f = -\frac{GMm}{r} - \frac{GMm}{r} = -\frac{2GMm}{r}$.Work done $W_{	ext{ext}} = U_f - U_i = -\frac{2GMm}{r} - (-\frac{4GMm}{r}) = \frac{2GMm}{r}$.

Column-$I$	Column-$II$
$(1)$ Can never be positive.	$(a)$ Escape velocity
$(2)$ Reason for negative potential energy of galaxies.	$(b)$ Gravitational potential energy
	$(c)$ The nature of force between different galaxies is attractive.

Similar Questions

Two bodies of mass $m$ and $9 m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero,will be ($G=$ gravitational constant):

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)

Match Column-$I$ with Column-$II$.
Column-$I$ Column-$II$
$(1)$ Can never be positive. $(a)$ Escape velocity
$(2)$ Reason for negative potential energy of galaxies. $(b)$ Gravitational potential energy
$(c)$ The nature of force between different galaxies is attractive.

Write $SI$ and $CGS$ unit of gravitational potential.

Give the difference between gravitational potential energy and gravitational potential.

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